arXiv research

Affirm Lord Rayleigh's conjecture on curved spaces for clamped plates.

The paper sets lower bounds for Laplacian eigenvalues and clamped plate problem eigenvalues.

This research optimizes plate structures to reduce vibrations in vehicles and aircraft.

In this paper, we study eigenvalues of a clamped plate problem. We obtain a lower bound for eigenvalues, which gives an important improvement of results due to Levine and Protter.

In this paper, we study estimates for eigenvalues of the clamped plate problem. A sharp upper bound for eigenvalues is given and the lower bound for eigenvalues in [10] is improved.

For a bounded domain $Ω$ in a complete Riemannian manifold $M^n$, we study estimates for lower order eigenvalues of a clamped plate problem. We obtain universal inequalities for lower order eigenvalues. We would like to remark that our results are sharp.

New isoperimetric inequality for clamped plates in RCD(0,N) spaces, sharp and stable.

This paper studies eigenvalues of the clamped plate problem on a bounded domain in an $n$-dimensional Euclidean space. We give an estimate for the gap between $\sqrt {Γ_{k+1}-Γ_{1}}$ and $\sqrt {Γ_{k}-Γ_{1}}$, for any positive integer $k$. According to the asymptotic formula of Agmon and Pleijel, we know, the gap betwe…

Extends plate problems to differential forms on manifolds.

The paper studies eigenvalue inequalities for a clamped plate problem involving a generalized elliptic differential operator.

Proves Payne conjecture for buckling and membrane eigenvalues.

We study Lord Rayleigh's problem for clamped plates on an arbitrary $n$-dimensional $(n\geq 2)$ Cartan-Hadamard manifold $(M,g)$ with sectional curvature $\textbf{K}\leq -κ^2$ for some $κ\geq 0.$ We first prove a McKean-type spectral gap estimate, i.e. the fundamental tone of any domain in $(M,g)$ is universally bounde…

Paper studies eigenvalues of a specific operator on Riemannian manifolds.

Sharp spectral gap estimates for higher-order operators on hyperbolic spaces.

In this paper, we establish sharp inequalities for four kinds of classical eigenvalues on a bounded domain of a Riemannian manifold. We also establish asymptotic formulas for the eigenvalues of the buckling and clamped plate problems. In addition, we give a negative answer to the Payne conjecture for the one-dimensiona…

In this paper, we establish universal inequalities for eigenvalues of the clamped plate problem on compact submanifolds of Euclidean spaces, of spheres and of real, complex and quaternionic projective spaces. We also prove similar results for the biharmonic operator on domains of Riemannian manifolds admitting spherica…

Sophie Germain's mean curvature deserves recognition as a surface shape measure.

The paper explores inequalities between eigenvalues on Riemannian manifolds.

Study proves inequalities for eigenvalues of fourth-order elliptic operators on Riemannian manifolds.

The Poisson problem consists in finding an immersed surface $Σ\subset\mathbb{R}^m$ minimising Germain's elastic energy (known as Willmore energy in geometry) with prescribed boundary, boundary Gauss map and area which constitutes a non-linear model for the equilibrium state of thin, clamped elastic plates originating f…

In this paper, we obtain a new abstract formula relating eigenvalues of a self-adjoint operator to two families of symmetric and skew-symmetric operators and their commutators. This formula generalizes earlier ones obtained by Harrell, Stubbe, Hook, Ashbaugh, Hermi, Levitin and Parnovski. We also show how one can use t…

The paper connects eigenvalue problems for various operators and establishes inequalities and asymptotic formulas for heat traces.

Improved lower bounds for poly-Laplacian eigenvalues in arbitrary dimensions.

The wave equation $u_{tt} = c^2 u_{xx}$ is generally regarded as a linear approximation to the equation describing the amplitude of a transversely vibrating elastic string in the plane. But, as is shown in \cite{BC96}, the assumption of transverse vibration in fact implies that the wave equation describes the vibration…

In Chinese societies, superstition is of paramount importance, and vehicle license plates with desirable numbers can fetch very high prices in auctions. Unlike other valuable items, license plates are not allocated an estimated price before auction. I propose that the task of predicting plate prices can be viewed as a …

The game of plates and olives, introduced by Nicolaescu, begins with an empty table. At each step either an empty plate is put down, an olive is put down on a plate, an olive is removed, an empty plate is removed, or the olives on two plates that both have olives on them are combined on one of the two plates, with the …

Transformer model predicts train axle vibrations for safer maintenance.

We examine the effect of clamping variables for approximate inference in undirected graphical models with pairwise relationships and discrete variables. For any number of variable labels, we demonstrate that clamping and summing approximate sub-partition functions can lead only to a decrease in the partition function e…

High throughput screening of compounds (chemicals) is an essential part of drug discovery [7], involving thousands to millions of compounds, with the purpose of identifying candidate hits. Most statistical tools, including the industry standard B-score method, work on individual compound plates and do not exploit cross…

Estimates for plate eigenvalues with nonzero Poisson's ratio.

This paper reviews traditional and modern methods for detecting structural damage using vibrations.

A wide class of machine learning algorithms can be reduced to variable elimination on factor graphs. While factor graphs provide a unifying notation for these algorithms, they do not provide a compact way to express repeated structure when compared to plate diagrams for directed graphical models. To exploit efficient t…

The paper analyzes the stability of an observer error in a vibrating string system.

In earlier work, we provided a general description of the forces of attraction and repulsion, encountered by two parallel vertical plates of infinite extent and of possibly differing materials, when partially immersed in an infinite liquid bath and subject to surface tension forces. In the present study, we examine som…

Study curves evolving by gradient flow of elastic energy, proving existence, smoothing, and convergence.

A novel ensemble classifier improves vibration-based quality monitoring accuracy.

CLAMP uses neural manifold packing to improve self-supervised learning.

Un sous-système de dimension différentielle au plus 2 d'une extension plate est plate. Si un tel système plat est stationnaire, il admet des sorties plates indépendantes du temps. A subsystem of a flat system of differential dimension at most 2 is flat. Furthermore, if such a flat system is stationary, we show that the…

Recent work by Jaffe and Scardicchio has expressed the optical approximation to the Casimir effect as a sum over geometric quantities. The first two authors have developed a technique which uses the complex geometry of the space of oriented affine lines in ${\Bbb{R}}^3$ to describe reflection of rays off a surface. Thi…

This work models variability in composite blades' vibrations.

Safe RL-based vibration control using LQR guidance.

PAVI speeds up Bayesian inference for large datasets.

The study focuses on the experiment of using three different smartphones to collect acceleration data from vibration for the road roughness detection. The Android operating system is used in the application. The study takes place on asphaltic pavement of the expressway system of Thailand, with 9 km distance. The run ve…

Study develops efficient algorithm for probabilistic penetration response of composite plates.

Euler's elastica with monotone curvature is uniquely minimal.

The paper proposes an ensemble of convolution-based methods for fault detection in gearboxes.

The study introduces a new stickiness parameter for stock prices using a non-linear model.

Paper proves rigidity estimates for hyperbolic shells and applies them to \(Γ\)-limit theory.